How to create a most basic texture on an object?
Most basic approach in Cycles:


Unwrap the cube in edit mode.

Create a new material.
In node editor, add an image texture and connect to material node.

View in render mode.



EDIT: You can make textures without nodes... sort of. And you can certainly make textures without using images. 

But Blender, Maya, 3ds etc are all node based. You can "hide" this fact by making settings in the data block areas, but nodes are what is really happening... which is to say changes you make in the materials property area, at right in image below, are actually just adjusting nodes. You don't have to "use" nodes, by which I mean see them, but they are their nonetheless.